Optical ranging has become an important capability for imaging systems, offering 3D reconstruction of standoff targets and enabling tasks such as, target identification, characterization and orientation. Optical ranging may be performed by laser or radar. Typically, laser ranging is performed using a short pulsed laser, and a high-speed photodetector, measuring time of flight of the optical pulse and then calculating the distance to the target, given the speed of optical pulse (light). However, in a photon starved regime, for example in the dark, the minimum error that can be achieved using this technique is large, requiring long acquisition times to achieve reliable estimate of range to target.
Recent work has shown the limited capabilities of laser ranging systems operating in the low-photon limit that employ coherent state sources and direct detection receivers. For example, see, Baris I. Erkmen, and Bruce Moision, “Maximum Likelihood Time-of-Arrival Estimation Of Optical Pulses Via Photon-Counting Photodetectors,” IEEE, ISIT 2009, Seoul, Korea, Jun. 28-Jul. 3, 2009 (hereinafter referred to as “[1]”), the entire contents of which are hereby expressly incorporated by reference.
For example, in [1], an analytic model for the mean-square error of a maximum likelihood (ML) estimator was developed. Then, two phenomena that cause deviations from a Cramer-Rao bound at low signal photon flux was illustrated. The model accurately predicts the ML performance over all regimes that we considered. An approximation to the threshold at which the ML estimator fails to provide better than a random guess of the pulse arrival time was also derived.